I solved the first part of that to give $x=1$, which I plugged back in and worked. But for the second part of the solution, $x$ could equal roughly $9.743156891$ or $0.1026361385$. Plugging them both into the original equation, I get the same on both sides. Yet, when I graphed it, the only solution, as far as I could see, is $1$.

I guess my real question is, are $9.74$ and $0.10$ actual solutions to the equation? Or are the extraneous for some reason?